Meshes went crazy (shaky)
Problem is gone after scaling up shaky objects and then scaling up all the stuff in the world to match the proportions accordingly. 

And the problem was not just clipping flickering since it caused real distortion, which was also visible in rendered view.

Thanks Everyone for the attention.

UPDATE: The real problem was the huge distance from the center of the project (grid).
So if you are having similar problems - try moving problematic stuff near the center.

Peace